9. Impulse and Response to Unit Impulse

Try these first

1. 1.

   What is an impulse in terms of forces?

   Hint

   Think about sudden forces in nature, like explosions.

2. 2.

   What does the Dirac delta function signify?

   Hint

   It can be thought of as a spike in a graph.

3. 3.

   What is the primary use of the Dirac delta function?

   • A) To define steady-state forces
   • B) To represent impulse forces
   • C) To calculate static loads

   Hint

   Consider when forces act briefly and with high magnitude.

4. 4.

   True or False: The impulse response function is used to determine how systems behave to arbitrary forces.

   • True
   • False

   Hint

   Think about how systems can react to any input based on their impulse behavior.

5. 5.

   Given a mass-spring-damper system with m = 2kg, c = 0.5 Ns/m, and k = 8 N/m, determine the response x(t) under unit impulse input.

   Hint

   Use the derived formulas for impulse response in your calculations.

6. 6.

   Explain the impact of increasing the damping ratio on the decay rate of oscillations in an SDOF system subjected to impulse.

   Hint

   Think about energy dissipation and system stability.